Related papers: Echo State Condition at the Critical Point

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…

The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of…

We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove at first a result on existence and uniqueness using form…

Supralinear and sublinear pre-synaptic and dendritic integration is considered to be responsible for nonlinear computation power of biological neurons, emphasizing the role of nonlinear integration as opposed to nonlinear output…

A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives…

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase…

In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction…

Link failures repeatedly induce large-scale outages in power grids and other supply networks. Yet, it is still not well understood, which links are particularly prone to inducing such outages. Here we analyze how the nature and location of…

In networked control, a fundamental problem is to determine the smallest capacity of a communication channel between a dynamical system and a controller above which a prescribed control objective can be achieved. Often, a preliminary task…

We view a neural network as a distributed system of which neurons can fail independently, and we evaluate its robustness in the absence of any (recovery) learning phase. We give tight bounds on the number of neurons that can fail without…

Network science is a rapidly expanding field, with a large and growing body of work on network-based dynamical processes. Most theoretical results in this area rely on the so-called \emph{locally tree-like approximation}. This is, however,…

This work considers a communication scenario where the transmitter chooses a list of size K from a total of M messages to send over a noisy communication channel, the receiver generates a list of size L and communication is considered…

While criticality is widely observed in neural networks, its underlying neural mechanism is not known well. We consider a network of $N$ excitatory leaky integrated and fire (LIF) neurons that reside on a regular lattice with periodic…

An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…

An upper bound on the feedback capacity of unifilar finite-state channels (FSCs) is derived. A new technique, called the $Q$-contexts, is based on a construction of a directed graph that is used to quantize recursively the receiver's output…

The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a…

Motivated by fading channels and erasure channels, the problem of reliable communication over deterministic relay networks is studied, in which relay nodes receive a function of the incoming signals and a random network state. An achievable…